Combinatorics on words has arisen independently within several branches of mathematics,
for instance, number theory, group theory and probability, and appears frequently in …

During the last two decades research on combinatorial problems of words, ie, on
Combinatorics on Words, has grown enormously. Although there has been important …

A vertex colouring of a graph $ G $ is" nonrepetitive" if $ G $ contains no path for which the
first half of the path is assigned the same sequence of colours as the second half. Thue's …

The two parts of this text are based on two series of lectures delivered by Jean Berstel and
Christophe Reutenauer in March 2007 at the Centre de Recherches Mathematiques …

A sequence a= a1a2… an is said to be nonrepetitive if no two adjacent blocks of a are
exactly the same. For instance, the sequence 1232321 contains a repetition 2323, while …

Th powerful (and so far under-utilized) Goulden—Jackson Cluster method for finding the
generating function for the number of words avoiding, as factors, the members of a …

We propose a new proof technique that aims to be applied to the same problems as the
Lov\'asz Local Lemma or the entropy-compression method. We present this approach in the …

Most modern implementations of regular expression engines allow the use of variables (also
called backreferences). The resulting extended regular expressions (which, in the literature …

Abstract Let $ g (n) $ be the length of a longest binary string containing at most $ n $ distinct
squares (two identical adjacent substrings). Then $ g (0)= 3$(010 is such a string), $ g (1) …

A sequence S= s1s2… sn is said to be nonrepetitive if no two adjacent blocks of S are the
same. A celebrated 1906 theorem of Thue asserts that there are arbitrarily long nonrepetitive …